Optimum three dimensional constellations for optical interconnects employing stokes vector receivers

Abstract

An optical modulation apparatus comprises first, second, and third optical modulators arranged so as to collectively modulate light coupled into a first optical input in all three dimensions of the three-dimensional Stokes vector space, to produce an optical output signal. The optical modulation apparatus further comprises a modulating circuit having a digital input configured to N generate first, second, and third modulating signals for driving the first, second, and third optical modulators so as to map digital data to an M-point optical constellation in the optical output signal. The points in the M-point optical constellation are distributed in the three-dimensional Stokes vector space such that the constellation figure of merit for the M-point optical constellation equals at least half of the maximum achievable constellation figure of merit for M points in the three-dimensional Stokes vector space.

What is claimed is: 
     
       1. An optical modulation apparatus, comprising:
 a first optical input configured for optical coupling to an output of a laser; 
 a first optical output configured for optical coupling to an optical fiber; 
 first, second, and third optical modulators having respective optical inputs, respective optical outputs, and respective analog inputs configured to receive respective modulating signals, wherein the first, second, and third optical modulators are arranged so as to collectively modulate light coupled into the first optical input in all three dimensions of the three-dimensional Stokes vector space, to produce an optical output signal at the first optical output; and 
 a modulating circuit having a digital input configured to receive digital data and having first, second, and third analog outputs electrically coupled to the analog inputs of the first, second, and third optical modulators and configured to generate first, second, and third modulating signals for driving the first, second, and third optical modulators so as to map the digital data to an M-point optical constellation in the optical output signal, the points in the M-point optical constellation being distributed in the three-dimensional Stokes vector space such that, given a constellation figure of merit defined as the ratio between the squared minimum distance and the average power of the constellation points, the constellation figure of merit for the M-point optical constellation equals at least half the maximum achievable constellation figure of merit for M points in the three-dimensional Stokes vector space. 
 
     
     
       2. The optical modulation apparatus of  claim 1 , wherein the points in the M-point optical constellation are distributed in the three-dimensional Stokes vector space such that the constellation figure of merit for the M-point optical constellation equals at least 90% of the maximum achievable constellation figure of merit for M points in the three-dimensional Stokes vector space. 
     
     
       3. The optical modulation apparatus of  claim 1 , wherein:
 the optical modulation apparatus further comprises an optical splitter configured to split light coupled from the laser, via the first optical input, into first and second portions; 
 the first and second optical modulators are in-phase and quadrature modulators configured to operate on the first portion of light, to generate an IQ-modulated optical signal; 
 the third optical modulator is a Mach-Zender intensity modulator configured to operate on the second portion of light coupled, to generate an intensity-modulated optical signal; 
 the optical modulation apparatus further comprises an optical combiner to combine the IQ-modulated optical signal and the intensity-modulated signal; and 
 the optical modulation apparatus is configured so that the IQ-modulated optical signal and the intensity-modulated signal have substantially orthogonal polarizations at the first optical output. 
 
     
     
       4. The optical modulation apparatus of  claim 1 , wherein:
 the optical modulation apparatus further comprises an optical splitter configured to split light coupled from the laser, via the first optical input, into first and second portions; 
 the first and second optical modulators are a Mach-Zender intensity modulator and an optical phase modulator configured to operate in series on the first portion of light, to generate an intensity- and phase-modulated optical signal; 
 the third optical modulator is a Mach-Zender intensity modulator configured to operate on a second portion of light coupled from the laser, to generate a second intensity-modulated optical signal; 
 the optical modulation apparatus further comprises an optical combiner to combine the intensity and phase modulated optical signal and the second intensity-modulated signal; and 
 the optical modulation apparatus is configured so that the intensity and phase modulated optical signal and the second intensity-modulated signal have substantially orthogonal polarizations at the first optical output. 
 
     
     
       5. The optical modulation apparatus of  claim 1 , wherein the first optical modulator is a Mach-Zender intensity modulator configured to modulate light from the first optical input;
 the second optical modulator is a Mach-Zender modulator configured to modulate the power difference between first and second orthogonal polarizations of light output from the first modulator; and 
 the third optical modulator is a Mach-Zender intensity modulator configured to modulate a phase of the first polarization or the second polarization of light output from the second optical modulator. 
 
     
     
       6. The optical modulation apparatus of  claim 1 , wherein the M-point constellation is a 16-point constellation, with the points arranged according to a hexagonal-close-packed (HCP) lattice or face-centered cubic (FCC) lattice. 
     
     
       7. The optical modulation apparatus of  claim 1 , wherein the M-point constellation is a 64-point constellation, with the points arranged according to a hexagonal-close-packed (HCP) lattice or face-centered cubic (FCC) lattice. 
     
     
       8. An optical transmitter, comprising:
 a laser having an output; 
 a first optical input configured for optical coupling to the output of the laser; 
 a first optical output configured for optical coupling to an optical fiber; 
 first, second, and third optical modulators having respective optical inputs, respective optical outputs, and respective analog inputs configured to receive respective modulating signals, wherein the first, second, and third optical modulators are arranged so as to collectively modulate light coupled into the first optical input in all three dimensions of the three-dimensional Stokes vector space, to produce an optical output signal at the first optical output; and 
 a modulating circuit having a digital input configured to receive digital data and having first, second, and third analog outputs electrically coupled to the analog inputs of the first, second, and third optical modulators and configured to generate first, second, and third modulating signals for driving the first, second, and third optical modulators so as to map the digital data to an M-point optical constellation in the optical output signal, the points in the M-point optical constellation being distributed in the three-dimensional Stokes vector space such that, given a constellation figure of merit defined as the ratio between the squared minimum distance and the average power of the constellation points, the constellation figure of merit for the M-point optical constellation equals at least half the maximum achievable constellation figure of merit for M points in the three-dimensional Stokes vector space. 
 
     
     
       9. An optical receiver apparatus, comprising:
 a Stokes vector receiver having an optical input configured to be coupled to an optical fiber, the Stokes vector receiver being configured to generate sampled data corresponding to the S1, S2, and S3 Stokes parameters of an optical signal received via the optical input; and 
 a digital processing circuit configured to demodulate digital data from the sampled data according to a modulation alphabet corresponding to an M-point optical constellation, the points in the M-point optical constellation being distributed in the three-dimensional Stokes vector space such that, given a constellation figure of merit defined as the ratio between the squared minimum distance and the average power of the constellation points, the constellation figure of merit for the M-point optical constellation equals at least half the maximum achievable constellation figure of merit for M points in the three-dimensional Stokes vector space. 
 
     
     
       10. The optical receiver apparatus of  claim 9 , wherein the M-point constellation is a 16-point constellation, with the points arranged according to a hexagonal-close-packed (HCP) lattice or face-centered cubic (FCC) lattice. 
     
     
       11. The optical receiver apparatus of  claim 9 , wherein the M-point constellation is a 64-point constellation, with the points arranged according to a hexagonal-close-packed (HCP) lattice or face-centered cubic (FCC) lattice.